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    Please help with this question

    What is the volume of the solid generated when the area of the curve y=3-3^x is rotated about the x axis

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    Junior Member HeroWise's Avatar
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    Re: Please help with this question

    Any ordinates given or assuming first quadrant?


    Use the powerful Blue Eyes White logs pls don't kill me
    Last edited by HeroWise; 20 Jan 2018 at 8:31 PM.

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    Re: Please help with this question

    Quote Originally Posted by kpad5991 View Post
    What is the volume of the solid generated when the area of the curve y=3-3^x is rotated about the x axis
    Infinity.

    If bounds are given, use the formula



    and use

    (for all )

    (remember to give your answers in cubic units!)
    Last edited by fan96; 20 Jan 2018 at 10:05 PM.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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    Junior Member HeroWise's Avatar
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    Re: Please help with this question

    Well to summ wat the above posts states is the

    x = e ^ (lnx)

    is the same thing right?

    didnt finish it fully, should be right if i didnt make silly errors, but you want to reach there
    Last edited by HeroWise; 20 Jan 2018 at 11:01 PM.

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    Taking a break! dan964's Avatar
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    Re: Please help with this question

    Herowise one of your coefficients is not correct.

    Quote Originally Posted by HeroWise View Post
    Well to summ wat the above posts states is the

    x = e ^ (lnx)

    is the same thing right?

    didnt finish it fully, should be right if i didnt make silly errors, but you want to reach there
    that is some funky integration going on there:

    Might be easier to use change of base before integrating. Also maybe leave the exponent as x rather than x+1 before integrating. Less likely to make mistakes that way.
    I'll do an improper integral here:






    or














    This is the improper integral. The integral with limits is done in a similar fashion.

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    Junior Member HeroWise's Avatar
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    Re: Please help with this question

    Pfft i feel dumb, i see where i went wrong, thanks a lot anyway @dan964


    EDIT: Wait, no i got the same result as yours @dan964, but i didnt simplify it. if i had, it would come down to your answer, and the ordinates, as i said, im geussing the question is asking for first quadrant, i remember a similar question while going over the Cambridge book, so i just "geussed". That isnt really good but i think the working should suffice the OP
    Last edited by HeroWise; 22 Jan 2018 at 11:23 AM.

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    Re: Please help with this question

    Quote Originally Posted by dan964 View Post
    Herowise one of your coefficients is not correct.



    that is some funky integration going on there:

    Might be easier to use change of base before integrating. Also maybe leave the exponent as x rather than x+1 before integrating. Less likely to make mistakes that way.
    I'll do an improper integral here:






    or














    This is the improper integral. The integral with limits is done in a similar fashion.
    This is what I got you will see the question from the textbook and my solutions I can't seem to get 13c. The books solution is pi(9-8/log3) u^3
    https://imgur.com/gallery/u5PCA

    Can someone please write the full solution to 13c

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    Junior Member HeroWise's Avatar
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    Re: Please help with this question

    Can you tell us the ordinates then, because as the working out provided by both @dan964 and i are elligible, so just put in the ordinates like normal integration, or provide us with ordinates; thatd be helpful for us ty

    or send a pic of the whole excercise

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    Re: Please help with this question











    Remember,







    Last edited by fan96; 22 Jan 2018 at 1:33 PM.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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